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leetcode/algorithms/cpp/singleNumber/singleNumber.II.cpp at master · fallleaves/leetcode · GitHub
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singleNumber.II.cpp
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//
Source : https://oj.leetcode.com/problems/single-number-ii/
//
Author : Hao Chen
//
Date : 2014-06-17
/*
*********************************************************************************
*
* Given an array of integers, every element appears three times except for one. Find that single one.
*
* Note:
* Your algorithm should have a linear runtime complexity. Could you implement it without using extra memory?
*
*
*********************************************************************************
*/
class
Solution
{
public:
Solution
(){
srand
(
time
(
0
));
}
//
random invoker
int
singleNumber
(
int
A[],
int
n) {
if
(
rand
()%
2
){
return
singleNumber_1
(A, n);
}
return
singleNumber_2
(A, n);
}
/*
* This solution is clear & straightforward implementation.
*
* We use an array of 32 length(e.g. count[32]) to count the the bits for all of numbers.
*
* Because the same number appear 3 times, which means the sum of i-th bits for all numbers should be 3 times.
*
* In other word, the sum of the i-th bits mod 3, it must be 0 or 1. 1 means that is the single number bit.
*
* This solution can be easy to extend to "every element appears k times except for one."
*
*/
int
singleNumber_1
(
int
A[],
int
n) {
int
count[
32
] = {
0
};
int
result =
0
;
for
(
int
i =
0
; i <
32
; i++) {
for
(
int
j =
0
; j < n; j++) {
if
((A[j] >> i) &
1
) {
count[i]++;
}
}
result |= ((count[i] %
3
) << i);
}
return
result;
}
/*
* The following solution is popular solution on Internet, but it looks it's not easy to understand.
*
* Actually, it just optimizes the above soultion.
*
* Let's see how it improve the above.
*
* We use three bitmasks,
* 1) `ones` as a bitmask which represents the i-th bit had appeared once.
* 2) `twos` as a bitmask which represents the i-th bit had appeared twice.
* 3) `threes` as a bit mask which represents the i-th bit had appeared three times.
*
* When the i-th bit had appeared for the third time, clear the i-th bit of both `ones` and `twos` to 0.
* The final answer will be the value of `ones`
*
*/
int
singleNumber_2
(
int
A[],
int
n) {
int
ones =
0
, twos =
0
, threes =
0
;
for
(
int
i =
0
; i < n; i++) {
//
`ones & A[i]` the result is the bitmask which the bits appeared twice
twos |= ones & A[i];
//
XOR means remove the bit which appeared twice int `ones`
ones ^= A[i];
//
count the `three`
threes = ones & twos;
//
clear the `ones` and `twos` if the i-th bit had appeared three times.
ones &= ~threes;
twos &= ~threes;
}
return
ones;
}
};
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